Near-field electrohydrodynamic jet (E-jet) printing has recently gained significant interest within the manufacturing research community because of its ability to produce micro/submicron-scale droplets using a wide variety of inks and substrates. However, the process currently operates in open-loop and as a result suffers from unpredictable printing quality. The use of physics-based, control-oriented process models is expected to enable closed-loop control of this printing technique. The objective of this research is to perform a fundamental study of the substrate-side droplet shape-evolution in near-field E-jet printing and to develop a physics-based model of the same that links input parameters such as voltage magnitude and ink properties to the height and diameter of the printed droplet. In order to achieve this objective, a synchronized high-speed imaging and substrate-side current-detection system is implemented to enable a correlation between the droplet shape parameters and the measured current signal. The experimental data reveals characteristic process signatures and droplet spreading regimes. The results of these studies served as the basis for a model that uses the measured current signal as its input to predict the final droplet diameter and height. A unique scaling factor based on the measured current signal is used in this model instead of relying on empirical scaling laws found in prior E-jet literature. For each of the three inks tested in this study, the average error in the model predictions is under 10% for both the diameter and the height of the steady-state droplet. While printing under nonconducive ambient conditions of low relative humidity and high temperature, the use of the environmental correction factor in the model is seen to result in a 17% reduction in the model prediction error.